Details

Time bar (total: 7.1s)

analyze99.0ms (1.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%24.7%75.3%0
0%24.7%75.3%1
0%24.7%75.3%2
12.4%12.4%75.3%3
12.4%12.4%75.3%4
18.5%6.2%75.3%5
18.5%6.2%75.3%6
21.6%3.1%75.3%7
21.6%3.1%75.3%8
23.2%1.5%75.3%9
23.2%1.5%75.3%10
23.9%0.8%75.3%11
23.9%0.8%75.3%12
24.3%0.4%75.3%13
24.3%0.4%75.3%14
Compiler

Compiled 35 to 18 computations (48.6% saved)

sample1.5s (21.8%)

Alt Table
StatusErrorProgram
0.2b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
Results
1.4s8256×body128valid
Compiler

Compiled 154 to 75 computations (51.3% saved)

localize35.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))
0.0b
(*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))))
0.1b
(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
0.1b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))

series222.0ms (3.1%)

Counts
4 → 96
Calls

4 calls:

171.0ms
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
26.0ms
(*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))))
13.0ms
(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
12.0ms
(+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))

rewrite83.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
726×prod-diff_binary32
198×log1p-udef_binary32
135×add-sqr-sqrt_binary32
129×egg-rr
126×add-log-exp_binary32
Counts
4 → 129
Calls

4 calls:

80.0ms
(+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))
80.0ms
(*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))))
80.0ms
(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
80.0ms
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01297
126753
2316353
3494753
000
100

prune381.0ms (5.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3647371
Fresh000
Picked101
Done000
Total3657372
Error
0.1b
Counts
372 → 7
Alt Table
StatusErrorProgram
5.2b
(exp.f32 (-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))))
14.3b
(*.f32 (cbrt.f32 (/.f32 (exp.f32 (/.f32 x s)) (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))) (pow.f32 (cbrt.f32 (/.f32 (exp.f32 (/.f32 x s)) (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))) 2))
0.7b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (exp.f32 (log1p.f32 (exp.f32 (/.f32 x s))))))
14.7b
(/.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (/.f32 x s)) 2)) (cbrt.f32 (/.f32 x s))) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
14.2b
(pow.f32 (/.f32 (sqrt.f32 (exp.f32 (/.f32 x s))) (*.f32 (sqrt.f32 s) (+.f32 (exp.f32 (/.f32 x s)) 1))) 2)
0.2b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
14.1b
(*.f32 (/.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 2) (*.f32 s (+.f32 (exp.f32 (/.f32 x s)) 1))) (/.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) (+.f32 (exp.f32 (/.f32 x s)) 1)))
Compiler

Compiled 10622 to 4281 computations (59.7% saved)

localize57.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)
0.1b
(exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))
0.1b
(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
0.1b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))

series209.0ms (3%)

Counts
4 → 64
Calls

4 calls:

172.0ms
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
15.0ms
(pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)
11.0ms
(exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))
10.0ms
(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))

rewrite86.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
944×prod-diff_binary32
182×add-sqr-sqrt_binary32
174×log1p-expm1-u_binary32
174×expm1-log1p-u_binary32
171×add-log-exp_binary32
Counts
4 → 112
Calls

4 calls:

82.0ms
(pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)
82.0ms
(exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))
82.0ms
(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
82.0ms
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01977
137952
2400252
3585652
000
100

prune288.0ms (4.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2102212
Fresh246
Picked011
Done000
Total2127219
Error
0.1b
Counts
219 → 7
Alt Table
StatusErrorProgram
0.2b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
14.1b
(*.f32 (exp.f32 (/.f32 x s)) (/.f32 1 (*.f32 s (+.f32 1 (*.f32 (exp.f32 (/.f32 x s)) (+.f32 2 (exp.f32 (/.f32 x s))))))))
10.9b
(/.f32 (pow.f32 (pow.f32 (exp.f32 -1) (pow.f32 (cbrt.f32 (/.f32 x s)) 2)) (cbrt.f32 (/.f32 x s))) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
5.2b
(exp.f32 (-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))))
14.3b
(*.f32 (cbrt.f32 (/.f32 (exp.f32 (/.f32 x s)) (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))) (pow.f32 (cbrt.f32 (/.f32 (exp.f32 (/.f32 x s)) (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))) 2))
0.7b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (exp.f32 (log1p.f32 (exp.f32 (/.f32 x s))))))
14.7b
(/.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (/.f32 x s)) 2)) (cbrt.f32 (/.f32 x s))) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
Compiler

Compiled 7032 to 3612 computations (48.6% saved)

localize51.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(exp.f32 (/.f32 x s))
0.1b
(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
0.1b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (exp.f32 (log1p.f32 (exp.f32 (/.f32 x s))))))
1.6b
(log1p.f32 (exp.f32 (/.f32 x s)))

series918.0ms (13%)

Counts
4 → 84
Calls

4 calls:

456.0ms
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (exp.f32 (log1p.f32 (exp.f32 (/.f32 x s))))))
447.0ms
(log1p.f32 (exp.f32 (/.f32 x s)))
10.0ms
(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
5.0ms
(exp.f32 (/.f32 x s))

rewrite112.0ms (1.6%)

Algorithm
batch-egg-rewrite
Rules
389×prod-diff_binary32
335×fma-udef_binary32
290×fma-def_binary32
215×expm1-udef_binary32
215×log1p-udef_binary32
Counts
4 → 122
Calls

4 calls:

109.0ms
(exp.f32 (/.f32 x s))
109.0ms
(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
109.0ms
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (exp.f32 (log1p.f32 (exp.f32 (/.f32 x s))))))
109.0ms
(log1p.f32 (exp.f32 (/.f32 x s)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01668
133643
2330243
3497343
4490543
000
100

prune349.0ms (4.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2581259
Fresh145
Picked011
Done011
Total2597266
Error
0.1b
Counts
266 → 7
Alt Table
StatusErrorProgram
0.2b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
14.1b
(*.f32 (exp.f32 (/.f32 x s)) (/.f32 1 (*.f32 s (+.f32 1 (*.f32 (exp.f32 (/.f32 x s)) (+.f32 2 (exp.f32 (/.f32 x s))))))))
10.9b
(/.f32 (pow.f32 (pow.f32 (exp.f32 -1) (pow.f32 (cbrt.f32 (/.f32 x s)) 2)) (cbrt.f32 (/.f32 x s))) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
5.2b
(exp.f32 (-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))))
14.3b
(*.f32 (cbrt.f32 (/.f32 (exp.f32 (/.f32 x s)) (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))) (pow.f32 (cbrt.f32 (/.f32 (exp.f32 (/.f32 x s)) (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))) 2))
14.6b
(/.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (/.f32 x s)) 2)) (cbrt.f32 (/.f32 x s))) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (exp.f32 (log1p.f32 (exp.f32 (/.f32 x s))))))
0.7b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (exp.f32 (log1p.f32 (exp.f32 (/.f32 x s))))))
Compiler

Compiled 7818 to 3204 computations (59% saved)

localize36.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)
0.7b
(exp.f32 (-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))))
1.6b
(log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))
4.4b
(-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2))))

series835.0ms (11.8%)

Counts
4 → 96
Calls

4 calls:

650.0ms
(log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))
133.0ms
(-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2))))
40.0ms
(exp.f32 (-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))))
12.0ms
(pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)

rewrite101.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
740×prod-diff_binary32
228×log1p-udef_binary32
207×egg-rr
130×add-sqr-sqrt_binary32
127×log1p-expm1-u_binary32
Counts
4 → 207
Calls

4 calls:

94.0ms
(pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)
94.0ms
(exp.f32 (-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))))
94.0ms
(log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))
94.0ms
(-.f32 (/.f32 x s) (log.f32 (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01375
127273
2330273
3507473
000
100

prune309.0ms (4.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New3012303
Fresh044
Picked101
Done022
Total3028310
Error
0.1b
Counts
310 → 8
Alt Table
StatusErrorProgram
0.2b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
14.1b
(*.f32 (exp.f32 (/.f32 x s)) (/.f32 1 (*.f32 s (+.f32 1 (*.f32 (exp.f32 (/.f32 x s)) (+.f32 2 (exp.f32 (/.f32 x s))))))))
5.3b
(pow.f32 (E.f32) (-.f32 (/.f32 x s) (+.f32 (log.f32 s) (*.f32 2 (log1p.f32 (exp.f32 (/.f32 x s)))))))
5.4b
(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 x s) (+.f32 (log.f32 s) (*.f32 2 (log1p.f32 (exp.f32 (/.f32 x s))))))) 3))
10.9b
(/.f32 (pow.f32 (pow.f32 (exp.f32 -1) (pow.f32 (cbrt.f32 (/.f32 x s)) 2)) (cbrt.f32 (/.f32 x s))) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
14.3b
(*.f32 (cbrt.f32 (/.f32 (exp.f32 (/.f32 x s)) (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))) (pow.f32 (cbrt.f32 (/.f32 (exp.f32 (/.f32 x s)) (*.f32 s (pow.f32 (+.f32 (exp.f32 (/.f32 x s)) 1) 2)))) 2))
14.6b
(/.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (/.f32 x s)) 2)) (cbrt.f32 (/.f32 x s))) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (exp.f32 (log1p.f32 (exp.f32 (/.f32 x s))))))
0.7b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (exp.f32 (log1p.f32 (exp.f32 (/.f32 x s))))))
Compiler

Compiled 9303 to 4458 computations (52.1% saved)

regimes1.2s (17.2%)

Accuracy

Total 0.0b remaining (40.4%)

Threshold costs 0.0b (40.4%)

Counts
208 → 1
Compiler

Compiled 25417 to 15776 computations (37.9% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary32
*-commutative_binary32
sub-neg_binary32
neg-sub0_binary32
distribute-frac-neg_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01946
12846
23146
33346
43446
53346

end139.0ms (2%)

Compiler

Compiled 289 to 174 computations (39.8% saved)

Profiling

Loading profile data...